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Home Differentiation Derivatives of Rational Functions Examples Example 7: Power Rule for Negative Exponents
 
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Example 7: Power Rule for Negative Exponents

Assume that u and v depend on x. Given y = (uv)-2, find dy/dx in terms of du/dx and dv/dx.

Let s = uv, whence y = s-2. We have

dy = -2s-3 ds,
ds = u dv + v du.

Substituting,

dy = -2(uv)-3(u dv + v du),

and

02_differentiation-142.gif
Home Differentiation Derivatives of Rational Functions Examples Example 7: Power Rule for Negative Exponents

Last Update: 2006-11-15